{"title":"在所有维的最小线性斯坦纳树上","authors":"T. Snyder","doi":"10.1145/98524.98596","DOIUrl":null,"url":null,"abstract":"It is proved that the length of the longest possible minimum rectilinear Steiner tree of <italic>n</italic> points in the unit <italic>d</italic>-cube is asymptotic to Β<subscrpt><italic>d</subscrpt>n</italic> d-1/d, where Β<subscrpt><italic>d</italic></subscrpt>. In addition to replicating Chung and Graham's exact determination of Β<subscrpt>2</subscrpt> = 1, this generalization yields tight new bounds such as 1 ≤ Β<subscrpt>3</subscrpt> < 1.191 and 1 < Β<subscrpt>4</subscrpt> < √<italic>2</italic>.","PeriodicalId":113850,"journal":{"name":"SCG '90","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1990-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"On minimal rectilinear Steiner trees in all dimensions\",\"authors\":\"T. Snyder\",\"doi\":\"10.1145/98524.98596\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is proved that the length of the longest possible minimum rectilinear Steiner tree of <italic>n</italic> points in the unit <italic>d</italic>-cube is asymptotic to Β<subscrpt><italic>d</subscrpt>n</italic> d-1/d, where Β<subscrpt><italic>d</italic></subscrpt>. In addition to replicating Chung and Graham's exact determination of Β<subscrpt>2</subscrpt> = 1, this generalization yields tight new bounds such as 1 ≤ Β<subscrpt>3</subscrpt> < 1.191 and 1 < Β<subscrpt>4</subscrpt> < √<italic>2</italic>.\",\"PeriodicalId\":113850,\"journal\":{\"name\":\"SCG '90\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1990-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SCG '90\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/98524.98596\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SCG '90","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/98524.98596","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On minimal rectilinear Steiner trees in all dimensions
It is proved that the length of the longest possible minimum rectilinear Steiner tree of n points in the unit d-cube is asymptotic to Βdn d-1/d, where Βd. In addition to replicating Chung and Graham's exact determination of Β2 = 1, this generalization yields tight new bounds such as 1 ≤ Β3 < 1.191 and 1 < Β4 < √2.
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